Non-Abelian Topological Order in $s$-Wave Superfluids of Ultracold Fermionic Atoms

It is proposed that in $s$-wave superfluids of cold fermionic atoms with laser-field-generated effective spin-orbit interactions, a topological phase with gapless edge states and Majorana fermion quasiparticles obeying non-Abelian statistics is realized in the case with a large Zeeman magnetic field. Our scenario provides a promising approach to the realization of quantum computation based on the manipulation of non-Abelian anyons via an $s$-wave Feshbach resonance.

Figure 1

The band energy of the lattice Hamiltonian (1) with edges at $i_x=0$ and $i_x=50(=L)$. Here $k_y\in [-\pi ,\pi ]$ denotes the momentum in the $y$ direction. We set $t=1$, $\mu =-4$, $\lambda =0.5$, and $\psi =0.5$. $h$ are (a) $h=0$, (b) $h=0.5$, (c) $h=0.8$. The red thin line indicates a gapless chiral edge mode localized on the one side and green thick line a gapless chiral edge mode on the other side. They appear for $\sqrt{{\psi }^2+ϵ(0,0{)}^2}<h<\sqrt{{\psi }^2+ϵ(0,\pi {)}^2}$.

Figure 2

Setup of the confining optical potential for the ground state. $\nu =x$ or $y$. Bold up and down arrows indicate, respectively, the spin-up and spin-down states. In this figure, excited levels which mediate the hopping via two Raman lasers are not shown explicitly.